Analytical expressions of 3D Reconstruction By Invariant Reduction Of Optical Flow Parameters

Abstract

This paper investigates the geometrical structure of parameters extracted from an optical flow. The transformation law is given with respect to the camera rotation around its focus by considering infinitesimal transformations. The parameter transformations form a representation of the 3D rotation group. The parameter space is decomposed into invariant subspaces of irreducible representations, and the optical flow is accordingly decomposed into two parts. The 3D reconstruction is described in terms of invariants extracted by this process. Their geometrical interpretation is also given.